Question

Assume that the duration of human pregnancies can be described by a normal model with mean 262 days and standard deviation 13 days. Answer the following questions.

​A) What percentage of pregnancies should last between 255 and 260 ​days?

​B) At least how many days should the longest 30​% of all pregnancies​ last?

​C) Suppose a certain obstetrician is currently providing prenatal care to 30 pregnant women. Let y overbar represent the mean length of their pregnancies. According to the central limit​ theorem, what is the mean and standard deviation ​SD(y overbar​) of the normal model of the distribution of the sample​ mean, y overbar​?

D) What is the probability that the mean duration of these​ patients' pregnancies will be less than 259 ​days?

Answer 1

Thre percentage or probability is calculated using Z score as

a) Z at 255

and Z at 260

P(255<X<260)

=P(-0.54<Z<-0.15) is calculated using Z table shown below as

=0.4404-0.2946

=0.1458

b) For the longest 30 % the Zscore ccorresponding to the 0.30 value is

Z=0.53

so, by z score formula

c) if 30 is selcted then Sample mean will be= 262 and sample standard deviation will be

d) if the mean to be less than 259 then

Z score at mean=259

P(Mean<259)

=P(Z<-1.27)

=0.1020